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Operator algebras for higher rank analysis and their application to factorial languages

Lookup NU author(s): Dr Evgenios Kakariadis

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Abstract

© 2021, The Hebrew University of Jerusalem. We study strong compactly aligned product systems of ℤ+N over a C*-algebra A. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite). Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.

Publication metadata

Author(s): Dor-On A, Kakariadis ETA

Publication type: Article

Publication status: Published

Journal: Journal d'Analyse Mathematique

Year: 2021

Volume: 143

Pages: 555-613

Online publication date: 29/06/2021

Acceptance date: 03/06/2019

ISSN (print): 0021-7670

ISSN (electronic): 1565-8538

Publisher: Hebrew University Magnes Press

URL: https://doi.org/10.1007/s11854-021-0163-6

DOI: 10.1007/s11854-021-0163-6

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